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PROB. VI. 
Invenire quotenis tentaminibus futurtim ft probabile, ut even - 
tus aliquis bis contingdt]. pofito quod fint cafas a quibus frimo 
tent mine contingere foffit , & cafus b quibus foffit non-con * 
Unger e ; it a, ut ft A &b de event u contendant^ pojjint A & 
B aqua forte eventum affirm are & negare, 
S G LU T I 0 , 
Sit x numerus tentaminum, ergo per jam demonftrata patebit 
fore a + b\ x = 2 b x + 2 axb x ~' 1 . Sive faciendo a :b : : i : q t 
1 + j|* =2 + 7'. i“. Sit q =3 i, {£ erit x = 3. 2 0 . Sit 
5 infinita, 5 c erit x infinita : Pone x infinitam, & ~ = x, & erit 
1 4- x •+• 4-z 1 4 - &c. =2 4- 22s, adeoque x = Log. 2, 
4- Log. •, jam fi Log. 2. vocetur aquatio ifta in hanc 
Tluxionalem transformabitur =>. Si autem valor ipfiiis,z 
inveftigetur per Poteftates ipfius >, invenietur z = 1.678 proxi- 
me, ergo x Temper confiftet intra iimites 3 q 5 c 1.678? h fed x 
citiflime converget ad v. 6 7 8?, adeoque fi q ad 1 habuerit ratio- 
nem non adeo parvam,’poterit aflumi x == 1.678?. Si vero fit 
aliquadiifpicia ne x fit jufto minor, fubftituatur ipfius valor in 
trquatione 1 4- -j\ = 24- ~ & notStur error, fi quis fit 
notatu dignus, tunc augeatur. x aliquaiitulum, & fubftituatur 
valor fic au&us pro x in*pratdi£la asquatione, 8c notetur novus 
error, & ope duorum errorum, valor ipfius * poterit fatis 
accurate corrigi. q ; r j'J J o fi 
rntr X3 33 ; auiilx:up rnunifflcinoJ Euiefnun /• JiiS 
G g XEMP. 
